Commutativity degree of $\mathbb{Z}_p$≀$\mathbb{Z}_{p^n}

Journal of Linear and Topological Algebra

مقاله 7، دوره 01، شماره 01، خرداد 2012، صفحه 41-44   

نویسنده

M. Maghasedi^*

Islamic Azad University, Karaj Branch, Iran

چکیده

For a nite group G the commutativity degree denote by d(G) and dend:
$$d(G) =\frac{|\{(x; y)|x, y\in G,xy = yx\}|}{|G|^2}.$$
In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.

کلیدواژه‌ها

Presentation of groups؛ Finite groups؛ commutativity degree

مراجع

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[3] W. H. Gustafson, What is probility that two group elements commute?, Amer. Math. Monthly, 80 (1973), 1031-1034.

[4] M. R. Jones, Muliplcators of p-groups, Math. Z., 127 (1972), 165-166.

[5] M. R. Jones, Some inequalities for the muliplcator of nite group, Math. Soc. 39 (1973), 450-456.

[6] P. Lescot, Isoclinism classes and commutativity degrees of nite groups,J. Algebra , 177 (1995), 847-869.

[7] M. R. R. Moghaddam ,A. R. Salemkar and K. chiti n-isoclinism classes and n-nilpotency degree of finite groups ,Algebra colloquium, (12:2) (2005), 255-261.